The chain of culpability, in my view as an outsider, goes iwantmyname > BrandShield > Funko Pop.
Funko Pop hired BrandShield, but from what I understand they did so exactly because the latter does all the work without you having to intervene. Kind of like you hiring a lawyer and them using ChatGPT to present the case, full of errors and non-existent sources. The lawyer might have been acting on your behalf, but they didn’t really do so according to your intentions and their fuck up isn’t your fault. On first view I’d say BrandShield is a culprit here, but can’t be so sure about Funko Pop yet.
On the other hand, iwantmyname is absolutely at fault. They took down a client’s website without asking or recourse, then sat on their asses. That’s who you sue, because they’re the ones who ultimately had the power and made the decision that affected itch.io. If iwantmyname wants to sue BrandShield and/or Funk Pop or whatever else in turn, none of your concern. The one’s who hurt the business were iwantmyname by not doing due diligence or contacting the client but just automatically bending over.
Now if they should be sued in Britain or New Zealand, that’s for the lawyers to know.
In fact, all of this is for the lawyers to figure out. I’m not one. I’m merely expressing what makes logical sense to me, which could be incredibly wrong.
If you hire the bad lawyer and loose the case, the lawyer won't serve your penalty. If Funko authorizes anyone to represent them, they are responsible.